Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

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1 Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles with just edges in common. 9-1.G.1.3 Draw three-dimensional objects and calculate the surface areas and volumes of these figures (e.g. prisms, cylinders, pyramids, cones, spheres) as well as figures constructed from unions of prisms with faces in common, given the formulas foe these figures. 1. The vertices of square ABCD are the midpoints of the sides of a larger square. Find the perimeter and the area of square ABCD. Round to the nearest hundredth. C 5 cm D B A 5 cm To find the perimeter, find the length of one side of square ABCD. Each side of the square is the hypotenuse of an isosceles right triangle with sides measuring.5 cm. so The perimeter of the square is The diagonals of square ABCD are 5 cm. The area of the square is = 1.5 cm, or the area of the square. A B C D The perimeter of a square is four times the length of one side. The perimeter of a square is four times the length of one side. Correct! Use the formula to find the area of a rhombus with diagonals measuring 5 cm.

2 . Find the area of the composite figure. 9 ft 1 ft 18 ft 9 ft Find the area of each triangle. Find the area of the rectangle. Find the area of the composite figure. A B C D Add the areas of the triangles to the area of the rectangle. The area of the triangles are each one-half times the base times the height. Correct! The area of each triangle is one-half the base times the height 3. Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumferences of the two circles. Round to the nearest hundredth. 3 In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored. 3. Let circle S be the smaller circle, and circle L be the larger circle. Let the radius of circle S be x. Then the radius of circle L is 3 + x. Circumference of the smaller circle Circumference of the larger circle 3 Substitute 3.14 for. The difference is 9.4 units.

3 4. A frustum of a pyramid is a part of the pyramid with two parallel bases. The slant height of the frustum of the pyramid is half the slant height of the original square pyramid. Find the surface area of the original pyramid, the lateral area of the top of the pyramid, and the area of the top base of the frustum. Then, find the surface area of the frustum of the pyramid. 8 cm 3 cm 6 cm In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored 4. Step 1 Find the slant height of the original square pyramid. cm Step Find the surface area of the original pyramid. cm. cm. cm Step 3 Find the lateral area of the top of the pyramid. cm Step 4 Find the area of the top base of the frustum. cm Step 5 Find the surface area of the frustum of the pyramid. 8 cm 3 cm 6 cm cm

4 Name: Date: Per: Student Page: Geometry / Day # 13 Composite Figures Key 1. A home owner wants to make a new deck for his backyard. Redwood costs $5 per square foot. The units on the graph are in feet. How much will it cost to create the deck shown? y x a. $160 c. $00 b. $38 d. $190 Step 1 Find the area of the deck. Area of deck = area of parallelogram + area of rectangle + area of trapezoid Step Find the cost of the deck. Cost = (area of deck in square feet) (cost per square foot of redwood) A Correct! B Multiply this answer by the cost per square foot of the decking to find the total cost. C Find the total area of the deck by adding the areas of the parallelogram, rectangle, and trapezoid. Then multiply this answer by 5 to find the total cost. D Find the total area of the deck by adding the areas of the parallelogram, rectangle, and trapezoid. Then multiply this answer by 5 to find the total cost.

5 . Find the surface area of the composite figure. Round to the nearest hundredth. 1.5 in. 3 in. in. in. a c b d Find the lateral area. Find the areas of the ends of the composite figure. Find the surface area. A Correct! B Include the area of each end of the composite figure. C First, find the lateral area of the two cylinders. Then, add the result to the area of the ends of the composite figure. D Find the total area of all the faces and curved surfaces of the composite figure.

6 3. Find the shaded area. Round to the nearest tenth. 5 in. 6 in. a. c. b. d. Subtract half the area of the circle from the area of the rectangle. Area of rectangle: Area of half a circle: Area of figure: A B C D Correct! Subtract half the area of the circle from the area of the rectangle. Subtract half the area of the circle from the area of the rectangle. Subtract half the area of the circle from the area of the rectangle.

7 4. This is a plan for a backyard. A concrete patio is in the inner part. Its dimensions are 30 yd by 18 yd. This patio is to be surrounded by a strip of grass. The outer dimensions are 36 yd by 4 yd. Find the area of the grassed region. Sod costs $0.65 per square foot. How much will it cost to sod this area? 36 yd 4 yd In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored yd 4 yd Area of large rectangle area of small rectangle A = b h b h A = A = 34 yd Convert A = 916 yd ft to ft 1 ft 1 ft Multiply It will cost $1, for the sod.

8 5. Find the surface area of the composite figure. Round to the nearest square centimeter. 5 cm 15 cm 5 cm a. 550 cm c. 75 cm b. 656 cm d. 814 cm The height of the cone is. The slant height (l) of the cone is given by the Pythagorean Theorem, The lateral area of the cone is The lateral area of the cylinder is The base area of the cylinder is S = (cone lateral area) + (cylinder lateral area) + (base area).. A B C D Include the lateral area of the cylinder. Include the base area. Correct! The figure has just one base.

9 6. A silo of a barn consists of a cylinder with diameter of 10 m, a height of 0 m, and is capped by a hemisphere. Find the volume of the silo. d = 10 m 0 In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored. 6. Volume of a cylinder + volume of half a sphere d = 10 m r = 5 H = 0 1 4π r V = π r H V = m 3 0

10 7. Find the area of the figure. Find the perimeter of the figure. 6 m 1 m 8 m 14 m In the answer box provided, with words, graphs, tables or equations, show your solution to the problem. Only work within the answer box will be scored m 1 m 3 m 6 8 m 8 m 6 3 m 1 m Area of a trapezoid + Area of a rectangle + Area of half a circle hb ( 1 b) r A= + + bh+ π 6( ) π 7 A = A = 311 m 14 m Perimeter is the sum of all the sides Use the Pythagorean Theorem to find the missing legs of the trapezoid = x x = 6.7 dπ 14π Half the circumference = = P = half the circumference P = 67.4 m

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